Classifying binary quadratic forms using Clifford invariants

Abstract

We functorially identify similarity classes of line-bundle-valued quadratic forms on rank two vector bundles with isomorphism classes of pairs consisting of the degree zero and the degree one parts of the associated generalized Clifford algebras. As applications, we generalize the Gauss Composition and explore connections with Picard groups of quadratic algebras.

43 pages, Accepted in Proceedings of the Indian Academy of Sciences: Mathematical Sciences